More Extra Math Answers
Answers are in Bold.
Links to corresponding mathematical concepts are in Bold.
Questions 1 – 5: Calculator-Prohibited
1. At a hardware store, a hammer costs $4.25, a wrench costs $2.79, and a screwdriver costs $1.99. The store also offers the above items together as a special at a cost of $6.39. How much money is saved by ordering the special instead of ordering each item separately?
2. A cable tv company charges $55.00 a month for basic service. Pay-per-view movies cost $5.99 apiece. If a customer watches 17 pay-per-view movies in a month, how much will that monthly cable tv bill be?
3. What is -7 squared?
4. What is 79 ÷ 75 ? Give your answer in exponent form.
5. What is the simplified version of √6 × √16 ?
Questions 6 -49: Calculator-Allowed
6. At a print shop, a customer can order 7 different business cards, 6 different post cards, and 5 different flyers. How many different combinations of these items can the customer order?
7. The probability of precipitation is 30% on Monday, 40% on Tuesday, and 50% on Wednesday. In percent terms, what is the probability of precipitation on all three days?
8. A plane departed from Los Angeles at 9:30 AM Pacific Standard Time (PST) and arrived in New York at 7:30 PM Eastern Standard Time (EST). Taking into account the different time zones as depicted in the map above, how many hours did the flight take?
9. A crew worked from 5 a.m. to 6 p.m. cleaning up a toxic spill at a cost of $9482.33. How much was the crew paid per hour?
10. A car traveled 1105 kilometers from 8 a.m to 9 p.m. What was the car’s speed?
A. 13 kilometers per hour
B. 85 miles per hour
C. 13 miles per hour
D. 85 kilometers per hour
11. An office worker drinks from zero to ten cups of coffee a day over the course of ten days. The median number of cups of coffee drunk is 3.5. The mode number of cups of coffee drunk is 3. Place two additional X marks on the graph below consistent with this information.
12. In fractional terms, what is the probability of picking 58 yellow balls out of a total of 100 balls, the rest of which are not yellow?
13. Over the course of a month, Betty, a real estate agent, earned a 6% commission on the sale of a $125000 house. She was also paid $2000 for doing clerical work. How much did Betty earn that month?
14. In the image below, two triangles are in proportion. How long is Q?
Ratio and Proportion
15. In the map above, the scale is 1 inch : 250 miles. Also in the map, Columbia, South Carolina and Jackson, Mississippi are approximately 2.5 inches apart. In the real world, approximately how many miles are Columbia and Jackson apart?
16. A gamma ray is 1.4 × 10-12 mm wide. If visible light is 7.0 × 10-7 mm wide, how many gamma rays can be fitted into the same space occupied by visible light? Express your answer in scientific notation.
A. 5.0 × 10-19
B. 2.0 × 10-20
C. 2.0 × 10-6
D. 5.0 × 105
17. What is the value of 12y – 3x² when x = -9 and y = 4?
18. The cumulative rent R for a car is $39.00 a day d plus a one-time surcharge of $65. What is the value of R where R = 39d + 65 and the car is rented for 11 days?
19. $6500 is deposited in a bank at a rate of 4% for 7 years. How much interest is earned over this time?
20. What is -|-5|?
21. The number of cats in our neighborhood is 7 more than 6 times the number of mice m. Which expression represents the number of cats in our neighborhood in terms of m?
A. 7 < 6m
B. 6m + 7
C. 6m < 7
D. 6(m + 7)
22. A hospital employs 55 RNs and 125 LPNs. An RN earns $3000 more a month than an LPN. Let y represent the hospital’s total nursing salaries in any given month and x represent the salary of an LPN in any given month. Which expression represents y in terms of x?
A. y = 125x – 55(x – 3000)
B. y = 125x – 55(x + 3000)
C. y = 125x + 55(x – 3000)
D. y = 125x + 55(x + 3000)
23. A chef concocted 7 original recipes an hour plus 2 old family recipes for a total of 51 recipes. Given the equation 7h + 2 = 51, how many hours h did the chef spend concocting recipes?
24. A trucker spent $6423.00 for new tractor-trailer tires that cost $400.00 apiece. The trucker also applied $23.00 worth of coupons to his purchase. Given the equation 400t + 23 = 6423, how many tires t did the trucker buy?
25. A teenager must spend less than $100.00 on rides at the State Fair. Each ride costs $8.00. The entrance fee to the fair costs $12.00. Which inequality represents the number of rides r the teenager can ride?
A. 12r + 8 < 100
B. 8r + 12 ≤ 100
C. 8r + 12 < 100
D. 12r + 8 ≤ 100
26. A restaurant must generate at least $1475.00 a day in order to break even or make a profit. The restaurant spends $500.00 a day on food and supplies. The restaurant expects 65 customers a day. Which inequality represents the amount x the restaurant must charge each customer in order to break even or make a profit?
A. 500x + 65 ≥ 1475
B. 65x + 500 > 1475
C. 65x + 500 ≥ 1475
D. 1475x + 65 > 500
27. Which expression represents 5x + 2 > 7 multiplied by 2?
A. -10x + 4 < -14
B. 10x + 4 < 14
C. -10x – 4 < -14
D. 10x + 4 > 14
28. A stamp collector must spend less than $650.00 at a show. The show charges a $25.00 entrance fee. The collector plans to spend $125.00 on each stamp x at the show. Thus, the inequality 125x + 25 < 650 expresses the number of stamps the collector can buy. Plot all possible points representing the number of stamps the collector can buy within the parameters of the number line below.
29. A souvenir stand must generate more than $540.00 in order to make a profit. It spends $365.00 on supplies. The stand will charge $25.00 for every item x it sells. Thus, the inequality 25x + 365 > 540 expresses the number of items the stand must sell in order to make a profit. Plot all possible points representing the number of items the stand must sell within the parameters of the number line below.
30. Bob planted a tiny tree in his yard. After 3 weeks, the tree was 5 inches tall. After 7 weeks, the tree was 25 inches tall. If it grows at the same rate, how many inches tall will the tree be at week 10?
31. Which of the following pairs of lines are perpendicular?
A. y = x + 2 and y = -3x – 4
B. y = 3x – 4 and x + 2
C. y = 3x + 5 and y = 3x – 3
D. y = 3x + 5 and y = -3x – 3
32. Which of the following represents the point-slope form of the equation of a line passing through point (3, 5) with a slope of -6?
A. y + 5 = 6(x + 3)
B. y + 5 = -6(x + 3)
C. y – 5 = 6(x + 3)
D. y – 5 = -6(x – 3)
33. With reference to Question 32, which of the following represents the
slope-intercept form of the equation of the line?
A. y = -6x + 23
B. y = -6x – 23
C. y = 6x – 23
D. y = 6x + 23
34. The following table shows the age in years and height in inches of a boy and a girl. On the accompanying x-y coordinate grid, plot the points for the girl at ages 3 and 7.
35. With reference to Question 34, which of the following is the correct linear equation passing through the points plotted?
A. y = -2.75x – 28.75
B. y = -2.75x + 28.75
C. y = 2.75x + 28.75
D. y = 2.75x – 28.75
36. With reference to Question 34, the girl is given the present of a giant beach ball whose diameter is as tall as she is at age 7.
To the nearest hundredth of square foot, what is the surface area of the beach ball?
37. The fireman’s ladder in the image below is leaning against a wall. Its base is 240 feet from the wall. Its top is 100 feet up the wall. How long in feet is the ladder?
38. As in the image below, a snail can crawl 8.8 meters along a wall and then turn 90° to the left and crawl 6.6 meters along another wall. If the snail took a straight shortcut from the start to the end of these two walls, how much shorter in meters would the shortcut be than sticking to the walls?
39. For the quadratic equation 4x² – 8x + 3 = 0, what is x?
A. 1 and 3
B. 2 and -2
C. -0.5 and -1.5
D. 0.5 and 1.5
40. As in the image below, a pizza has a diameter of 15 inches. To the nearest tenth of an inch, what is its circumference?
41. As in the image below, a triangular wedge has an angle q that measures 43° and an angle r that measures 90°. What is the measurement of angle s (the triangular wedge’s third angle) in degrees?
42. As in the image below, a triangular billboard has a base of 4.4 meters and a height of 3.3 meters. What is its perimeter in meters?
43. As in the image below, the length of a rectangular dance hall is 12.5 meters and its width is 8.5 meters. What is the dance hall’s area in square meters?
44. As in the image below, a trapezoidal window is 500 centimeters tall and its parallel sides are 1200 and 800 centimeters long, respectively. What is its area in square meters?
45. As in the image below, a cinder block has a length of 120 centimeters, width 50 centimeters, and height 70 centimeters. What is its surface area in square meters?
Right Rectangular Prism
46. The dot plot below shows the minimum stock price of Facts and Figures Corporation from 2000 to 2014. What stock price represents the mode?
47. The following table shows the year and corresponding stock price for Facts and Figures Corporation. On the accompanying x-y coordinate grid, plot the points for the years 2009 and 2013.
|Facts and Figures Corporation|
48. With reference to Question 47, which of the following is the correct linear equation passing through the points plotted?
A. y = 3x + 5997
B. y = -3x – 5997
C. y = -3x + 5997
D. y = 3x – 5997
49. Because of his self-perceived success, the President of Facts and Figures Corporation decides to use company funds to build a humongous monument to himself in the shape of a pyramid. As in the figure below, the pyramid will have a square base. The distance along each side of the base will be 8 miles. The slant height of the pyramid will be 10 miles. What will be the lateral area of the pyramid in square miles?